Ambient occlusion problem using EEVEE
The reason for this happening is that unlike cycles, ambient occlusion generated by evvee are not physically accurate. Eevee tries to mimic ambient occlusion and only generates ambient occlusion for objects in front of the camera.
As you said, ambient occlusion pops occurs when an object which was hidden by something comes in front of the camera. It is coz as soon as the object is visible to camera, eevee generates ambient occlusion causing the poping effect.
My advice would be to use cycles which generates physically accurate Ao maps